1. Field of the Invention
This invention relates to the field of earth borehole logging and, more particularly, to a method and apparatus for determining properties of anisotropic earth formations. Properties that can be determined using the invention include horizontal conductivity, vertical conductivity, horizontal dielectric constant, vertical dielectric constant, and dip angle.
2. Description of the Related Art
The well logging art has recognized for many years that formations surrounding an earth borehole can be anisotropic with regard to conduction of electrical currents (see e.g. K. S. Kunz et al., "Some Effects Of Formation Anisotropy On Resistivity Measurements In Boreholes", Geophysics, Vol. 23, No. 4, 1958). The phenomenon of electrical anisotropy is generally visualized in one of two ways, or a combination thereof, as follows.
In many sedimentary strata, electric current flows more easily in a direction parallel to the bedding planes than transversely to them. A reason for this anisotropy is that a great number of mineral crystals possess a flat or elongated shape (e.g. mica and kaolin). At the time they were laid down, they naturally took an orientation parallel to the plane of sedimentation. The interstices in the formations are, therefore, generally parallel to the bedding plane, and the current is able to travel with facility along these interstices which often contain electrically conductive mineralized water. Such electrical anisotropy, sometimes called microscopic anisotropy, is observed mostly in shales.
If a cylindrical sample is cut from a formation, parallel to the bedding planes, the resistivity of this sample measured with a current flowing along its axis is called the longitudinal (or horizontal) resistivity R.sub.h. The inverse of R.sub.h is the horizontal conductivity, .sigma..sub.h. If a similar cylinder is cut perpendicular to the bedding planes, the resistivity measured with a current flowing along its axis is called the transversal (or vertical) resistivity R.sub.v. The inverse of R.sub.v is the vertical conductivity, .sigma..sub.v. The anisotropy coefficient .lambda., by definition, is equal to .sqroot.R.sub.v /R.sub.h (or .sqroot..sigma..sub.h /.sigma..sub.v ). Laboratory measurements have shown that .lambda. may range from 1 to about 2.5 in different shales.
Furthermore, the formations are often made up of a series of relatively thin beds having different lithologic characteristics and, therefore, different resistivities (as, for example, sequences of thin shales and hard streaks). In well logging systems the distances between the electrodes or antennas are great enough that the volume involved in a measurement may include several such thin beds. Since, in this situation, the current flows more easily along the more conductive streaks than transversely to the series of beds, there is effective anisotropy. The effects on resistivity measurements of this "macroscopic" anisotropy are cumulative with the effects of the anisotropy due to the above-described microscopic structure of the sediments. Reference can also be made to J. H. Moran et al., "Effects Of Formation Anisotropy On Resistivity Logging Measurements", Geophysics, Vol. 44, No. 7, 1979, and to R. Chemali et al., "The Effect Of Shale Anisotropy On Focused Resistivity Devices", SPWLA Twenty-Eighth Annual Logging Symposium, 1987.
The determination of R.sub.v as well as R.sub.h can be useful in various situations. For example, consider the case where the formation consists substantially of two types of material with resistivities R.sub.1 and R.sub.2 with respective volume fractions .alpha. and 1-.alpha.. The effective horizontal and vertical resistivities R.sub.h and R.sub.v are given by ##EQU1## If .alpha. is known, such as in a shale sequence where a gamma ray measurement or a spontaneous potential measurement has been used to provide the shale fraction, R.sub.1 and R.sub.2 can be determined from (1) and (2) if R.sub.h and R.sub.v are known.
In situations where the borehole intersects the formations substantially perpendicular to the bedding planes, conventional induction and propagation well logging tools are sensitive almost exclusively to the horizontal components of the formation resistivity. When the borehole intersects the bedding planes at an angle, the tool readings contain an influence from the vertical resistivity as well as the horizontal. This is particularly true when the angle between borehole and the normal to the bedding planes becomes large, such as in directional or horizontal drilling where angles near 90.degree. are commonly encountered. In these cases, the influence of vertical resistivity can cause discrepancies between measurements in these wells and measurements taken of the same formation in nearby vertical wells, thereby preventing useful comparison of these measurements. In addition, since reservoir evaluation is typically based upon data from vertical wells, use of data from wells drilled at high angles may produce erroneous estimates of formation producibility if proper account is not taken of the anisotropy effect.
A number of techniques have been proposed for measuring formation anisotropy and/or vertical conductivity, such as by providing transmitter and/or receiver coils that are perpendicular to the borehole axis in addition to coils having conventional orientations. Reference can be made, for example, to U.S. Pat. Nos. 4,302,722, 4,302,723, and 4,980,643.
Equipment and techniques that determine horizontal and vertical conductivity (or anisotropy) by employing special equipment dedicated specifically to such purpose result in increased equipment cost and increased logging time and/or cost. U.S. Pat. No. 5,329,448 discloses a technique for determining horizontal and vertical conductivity (or anisotropy determinable therefrom) using measurements that are often available from conventional types of equipment utilized for logging earth boreholes during drilling or by wireline. In the '448 Patent, first and second formation conductivity values are derived from measurements taken in a borehole. The derived first and second formation conductivity values are obtained from measurements which are affected differently by the vertical and horizontal conductivities of the formations. These may be, for example, conductivities respectively obtained from phase and attenuation measurements from a receiver pair of a propagation logging device such as that disclosed in U.S. Pat. No. 4,899,112, or conductivities respectively obtained from the resistive and reactive components of an induction logging apparatus. Horizontal and vertical conductivity model values are selected, and error values are computed from the differences between: (i) first and second composite conductivity values computed as a function of the horizontal and vertical conductivity model values, and (ii) the first and second derived formation conductivity values. In iterative fashion, the model values are modified in a manner that tends to reduce the error values. The '448 Patent continues the process until a predetermined criterion of the error is met, whereupon the modified horizontal and vertical conductivity model values can be read out as the determined values.
It is among the objects of the present invention to provide a method and apparatus for determining properties of anisotropic earth formations that improves on prior techniques for determination of horizontal and vertical conductivity and is also capable of providing dip angle and anisotropic dielectric constant characteristics.